Optimal identification experiment design for the interconnection of locally controlled systems

Bombois, Xavier; Korniienko, Anton; Hjalmarsson, Håkan; Scorletti, Gérard

doi:10.1016/j.automatica.2017.12.014

Cited by 6 publications

(28 citation statements)

References 28 publications

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“…To do so, we adapt the hierarchical robustness analysis approach of [12]-[14], initially proposed in [15], to the class of uncertainties obtained from system identification. A similar subject is presented in our current work [16]. The main contribution of this technical report is, however, a deeper investigation of the robustness analysis aspects, allowing, in contrast to [16], for several types of embedding and their combinations.The next section of the technical report formulates the problem under consideration, while the third section presents the main result of the technical report, the hierarchical analysis approach.…”

mentioning

confidence: 73%

“…A similar subject is presented in our current work [16]. The main contribution of this technical report is, however, a deeper investigation of the robustness analysis aspects, allowing, in contrast to [16], for several types of embedding and their combinations.The next section of the technical report formulates the problem under consideration, while the third section presents the main result of the technical report, the hierarchical analysis approach. The fifth section is dedicated to the numerical illustration example and the last section concludes the technical report.…”

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confidence: 73%

“…As is shown in the proof of Lemma 1, the result of [13] is adapted to the case of uncertain vectors that belong to an ellipsoid which recovers sufficient and necessary conditions of {x(ω), y(ω), z(ω)} -dissipativity. This lemma is an extension of the robustness analysis result of [16] and will be used to generate different types of embeddings.…”

Section: B Local Stepmentioning

confidence: 99%

“…To satisfy this constraint, first an identification procedure is performed leading to a consistent parameter vector estimatê θ i of each subsystem true parameter vector θ i,0 as well as an estimation of the corresponding covariance matrices P θi ensuring (7). Due to the presence of a double integrator in the car transfer function model, this identification experiment has to be performed in closed loop with a stabilizing controller either independently for each module (see [2], [11]) or in the network (see [16]). The results of the latter method are presented in Fig.…”

Section: Numerical Examplementioning

confidence: 99%

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Hierarchical Robust Analysis for Identified Systems in Network

et al. 2018

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This technical report considers worst-case robustness analysis of a network of locally controlled uncertain systems with uncertain parameter vectors belonging to the ellipsoid sets found by identification procedures. In order to deal with computational complexity of large-scale systems, an hierarchical robustness analysis approach is adapted to these uncertain parameter vectors thus addressing the trade-off between the computation time and the conservatism of the obtained result. I. INTRODUCTIONIn this technical report, the problem of worst-case robustness analysis of a network of locally controlled uncertain Linear Time Invariant (LTI) subsystems is under consideration. The uncertainty of each subsystem is an uncertain real vector that belongs to an ellipsoid: an uncertainty set in the model parameter space typically obtained after identification.This work is motivated by recent technological advances in Microelectronics, Computer Sciences, Robotics, and related topics in the field of the Multi-Agent systems [1]. The control of these network systems is usually decentralized and in order to compute controllers achieving high performance level, the model of the subsystems needs to be known. An efficient method to build the appropriate models is system identification [2]. However, due to the presence of the noise and since the identification experiment is limited in time, the model parameters can only be identified within some prescribed uncertainty region which is typically an ellipsoid. For these reasons, in order to ensure that the computed controllers achieve the performance not only for the nominal identified model but for the true network system, it is important to take into account these uncertainties. The evaluation of the uncertainty effects on the system stability and performance is called robustness analysis.The large scale of today's systems raises additional challenges on identification, controller design as well as on the robustness analysis. In this technical report we focus on the robustness analysis in the context of large-scale network systems.In the 80's-90's, µ-analysis [3], [4] was developed to investigate the performance of LTI systems in the presence of structured uncertainties. The performance is evaluated in the frequency domain [5]. This approach is based on the computation of the structured singular value µ of the frequency dependent matrices, which was proved to be NP-hard [6]. Fortunately, lower and upper bounds on µ can be efficiently computed; the µ upper bounds in [7] guarantee a certain level of performance with some conservatism. By efficient, it is understood that the computation time is bounded by a polynomial function of the problem size [8]. An adaptation of these results to classes of the uncertainties obtained by identification can be found in [9]- [11].Nevertheless, even if the computation of the µ upper bound is efficient, its computation time can be important in the case of uncertain large-scale systems. The purpose of this technical report is to extend the results [9]-[11...

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Section: B Local Stepmentioning

confidence: 99%

Section: Numerical Examplementioning

confidence: 99%

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Hierarchical Robust Analysis for Identified Systems in Network

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“…These methods have been extended only recently to networked systems [7], providing conditions for obtaining a consistent estimate of only one module inside the network [8]. Under certain conditions we can define an uncertainty region associated to the model, containing the true system [5], which can be used to design a controller that robustly ensures the network performance [9]. This uncertainty region can be shaped by a proper design of the external excitation signal used during the experiment.…”

Section: Introductionmentioning

confidence: 99%

Optimal Experiment Design for the Identification of One Module in the Interconnection of Locally Controlled Systems

Morelli

Bombois

Hjalmarsson³

et al. 2019

2019 18th European Control Conference (ECC)

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In this paper, we consider the problem of designing the least costly experiment that leads to a sufficiently accurate estimate of one module in a network of locally controlled systems. A module in such a network can be identified by exciting the corresponding local closed loop system. Such an excitation signal will not only perturb the input/output of the to-be-identified module, but also other modules due to the interconnection. Consequently, the cost of the identification can be expressed as the sum of the influence of the excitation signal on the inputs and outputs of all locally controlled systems. We develop a methodology to design the spectrum of the excitation signal in such a way that this cost is minimized while guaranteeing a certain accuracy for the identified model. We also propose an alternative identification configuration which can further reduce the propagation of the excitation signal to other modules and we make steps to robustify this optimal experiment design problem with respect to the cost of the identification.

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Separable multi‐innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems

Ding

Wan

et al. 2020

Adaptive Control & Signal

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SummaryThis article is concerned with the parameter identification problem of nonlinear dynamic responses for the linear time‐invariant system by means of an impulse excitation signal and discrete observation data. Using the impulse signal as the input, the impulse response experiment is carried out and the dynamical moving sampling is designed to generate the measured data for deriving new identification algorithms. By applying the moving window data that contain the dynamical information of the system to be identified, an objective function with respect to the parameters of the systems is constructed according to the impulse response. In accordance with different functional relations between the system parameters and the system output response, the unknown parameter vector of the system is separated into a linear parameter vector and a nonlinear parameter vector. Based on the separated parameter vectors, two subidentification models are constructed and a separable identification algorithm is presented through the gradient search to improve the accuracy. Moreover, for the purpose of enhancing the estimation accuracy and capturing the dynamical feature of the systems, the moving window data are employed to develop the separable identification algorithm. The performance of the proposed separable identification method is illustrated via a numerical example.

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Optimal identification experiment design for the interconnection of locally controlled systems

Cited by 6 publications

References 28 publications

Hierarchical Robust Analysis for Identified Systems in Network

Hierarchical Robust Analysis for Identified Systems in Network

Optimal Experiment Design for the Identification of One Module in the Interconnection of Locally Controlled Systems

Separable multi‐innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems

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